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Insphere Radius of Dodecahedron given Space Diagonal Formula

GoInsphere Radius of Dodecahedron Formula

GoInsphere Radius of Dodecahedron given Volume Formula

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Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere. Check FAQs

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{d Space}{\sqrt{3} \cdot (1 + \sqrt{5})}

r_i - Insphere Radius of Dodecahedron?d_Space - Space Diagonal of Dodecahedron?

Insphere Radius of Dodecahedron given Space Diagonal Example

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Here is how the Insphere Radius of Dodecahedron given Space Diagonal equation looks like with Values.

Here is how the Insphere Radius of Dodecahedron given Space Diagonal equation looks like with Units.

Here is how the Insphere Radius of Dodecahedron given Space Diagonal equation looks like.

11.1252 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{28}{\sqrt{3} \cdot (1 + \sqrt{5})}

11.1252m = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{28m}{\sqrt{3} \cdot (1 + \sqrt{5})}

11.1252 = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{28}{\sqrt{3} \cdot (1 + \sqrt{5})}

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Insphere Radius of Dodecahedron given Space Diagonal Solution

Follow our step by step solution on how to calculate Insphere Radius of Dodecahedron given Space Diagonal?

FIRST Step Consider the formula

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{d Space}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Substitute values of Variables

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{28m}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{28}{\sqrt{3} \cdot (1 + \sqrt{5})}

Next Step Evaluate

∴

r i = 11.1251626120847m

LAST Step Rounding Answer

∴

r i = 11.1252m

Insphere Radius of Dodecahedron given Space Diagonal Formula Elements

Variables

Functions

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Dodecahedron

Space Diagonal of Dodecahedron

The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Dodecahedron

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Insphere Radius of Dodecahedron

Go Insphere Radius of Dodecahedron

r i = \sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}} \cdot \frac{l e}{2}

Go Insphere Radius of Dodecahedron given Volume

r i = \frac{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Insphere Radius of Dodecahedron given Total Surface Area

r i = \sqrt{\frac{TSA \cdot (25 + (11 \cdot \sqrt{5}))}{120 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Insphere Radius of Dodecahedron given Face Area

r i = \sqrt{\frac{A Face \cdot (25 + (11 \cdot \sqrt{5}))}{10 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

How to Evaluate Insphere Radius of Dodecahedron given Space Diagonal?

Insphere Radius of Dodecahedron given Space Diagonal evaluator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))) to evaluate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Space Diagonal formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using space diagonal of Dodecahedron. Insphere Radius of Dodecahedron is denoted by r_i symbol.

How to evaluate Insphere Radius of Dodecahedron given Space Diagonal using this online evaluator? To use this online evaluator for Insphere Radius of Dodecahedron given Space Diagonal, enter Space Diagonal of Dodecahedron (d_Space) and hit the calculate button.

FAQs on Insphere Radius of Dodecahedron given Space Diagonal

What is the formula to find Insphere Radius of Dodecahedron given Space Diagonal?

The formula of Insphere Radius of Dodecahedron given Space Diagonal is expressed as Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))). Here is an example- 11.12516 = sqrt((25+(11*sqrt(5)))/10)*28/(sqrt(3)*(1+sqrt(5))).

How to calculate Insphere Radius of Dodecahedron given Space Diagonal?

With Space Diagonal of Dodecahedron (d_Space) we can find Insphere Radius of Dodecahedron given Space Diagonal using the formula - Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Insphere Radius of Dodecahedron?

Here are the different ways to Calculate Insphere Radius of Dodecahedron-

Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
Insphere Radius of Dodecahedron=sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron=sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))

Can the Insphere Radius of Dodecahedron given Space Diagonal be negative?

No, the Insphere Radius of Dodecahedron given Space Diagonal, measured in Length cannot be negative.

Which unit is used to measure Insphere Radius of Dodecahedron given Space Diagonal?

Insphere Radius of Dodecahedron given Space Diagonal is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Insphere Radius of Dodecahedron given Space Diagonal can be measured.

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